Question

Assume the prices of product X and Y are $1.50 and $1.00, respectively, and that Mr. Chen has $24 to spend. Assume a normal indifference curve. Assume that Mr. Chen needs 4 of product X to maximize utility.

a. What is the slope of Mr. Chen’s budget constraint.

b. Write out Mr.Chen’s equation to his budget constraint.

c. What combination of X and Y will Mr. Chen purchase?

d. Now assume that the price of Y changed from $1.00 to $2.00, redo part a, b and c,

e. Draw the budget constraint graph and indifference curve before the change and after the change in the price of Y. Explain the substitution and income effect for this change.

6. Now assume instead of a price change, Mr. Chen’s budget changed from $24 to $30, and the prices are still $1.50 and $1.00 for product X and Y respectively. Redo parts a, b, c and draw the before and after change on the budget constraint and indifference curve.

Answer 1

As per Chegg guidelines, I can solve only the first 4 questions at a time,

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the solution of the above question is,

$ 24 to spend

price of good X = $1.50

price of food Y = $ 1.00

Mr Chen needs 4 unit of product x to maximise utility.

a) The slope of budget: it shows how much consumer need to sacrifice of a good to gain an additional unit of another good Y. It describes by the ratio of prices goods.

slope = price of X / Price of Y = 1.50/1.00 = 1.50

it shows that an additional unit of X needs to sacrifice1.50 unit of good Y.

b) Equation of budget constraint

24 =1.50(X) + 1.00(Y) where X and Y show unit of good X and good y respectively.

c).already given to maximise the utility of Mr Chen it needs 4 unit of good X hence

put X=4 into the budget equation

24 = 1.50(4) + 1.00 (Y)

24 = 6 + Y

24 - 6 = Y

18 = Y

the combination is 4 unit of good X and 18 Unit of good y will Chen purchase to maximise his utility.

d.) if the price of good y changed from 1.00 to 2.00.

the slope of the budget line:

Slope = price of X / Price of Y = 1.50/2.00 = .75

it shows that an additional unit of X needs to sacrifice0.75 unit of good Y.

Budget equation:

24 =1.50(X) + 2.00(Y) where X and Y show unit of good X and good y respectively.

The Combination of Good X and Good Y

Already given to maximise the utility of Mr Chen it needs 4 unit of good X hence

put X=4 into the new budget equation

24 =1.50(4) + 2.00(Y)

24 = 6 + 2.00(Y)

24 - 6 = 2.00(Y)

Y = 18 / 2.00

Y = 9

the combination is 4 unit of good X and 9 Unit of good y will Chen purchase to maximise his utility with the new budget line.